A free Internet census index and images to the 1860 census can be viewed on the FamilySearch Record Search. This index shows every name listed on the census and is linked to census images including information about each person’s residence, age, birthplace, occupation, other family members, and neighbors.

For more details, see individual state census Wiki pages. For tips if the first census index search does not work, see the United States Census Searching Wiki page.

To use the Archive.org copy of the 1860 Census, look up the person you're looking for in the FamilySearch Index. Look up where the record is from (State & County), then use that to identify which Roll (in PDF format) to look in. There should be a page number in the index. It's not very convenient, but it works.

Alternatively, try this formula to build the address URL using FamilySearch record data:

Find the "GS Film Number" which looks like this, for example: 803590

Now, keep the last three digits: 803590 becomes 590

This is the FFF number.

Find the "Image Number" which looks like this, for example: 00280

Now, strip off the leading zeroes: 00280 becomes 280

This is the PPPP number (and can be 1 to 5 digits).

Insert the digits you just found into the following address in place of the FFF and PPPP characters:

http://archive.org/stream/populationscheduFFFunit#page/nPPPP/mode/1up

For example, using the above numbers, we get this:

http://archive.org/stream/populationschedu590unit#page/n280/mode/1up

Copy and paste that into a browser address bar and press enter. You will likely have to scroll up a page or two or three to find the right page. Use "Page" and "Household ID" data from the FamilySearch record to more easily find the right page and entry.